Qianxiao Li: Free-energy-like concepts for nonequilibrium systems; Cheng Tai: Video Super-Resolution via Adaptive Wavelet Frames and Elastic Deformations

Qianxiao Li: Free-energy-like concepts for nonequilibrium systems; Cheng Tai: Video Super-Resolution via Adaptive Wavelet Frames and Elastic Deformations

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Qianxiao Li & Cheng Tai - Special Grad Student Seminar, Princeton University
Fine Hall 214

Abstract: Qianxiao Li - The extension of the concept of free energy to fully nonequilibrium systems is an important problem in statistical mechanics. I will discuss how a straightforward generalization, using the nonequilibrium steady-state distribution in place of the canonical ensemble, yields a free energy that is not sufficient in capturing the dynamics of general nonequilibrium steady states. One can overcome this problem by defining the "free action", which is like a trajectory-space free energy. Through a representative example, I will discuss the conceptual and practical usefulness of the free action in quantifying the dynamics of nonequilibrium steady states. If time allows, I will also discuss how one can employ similar ideas to treat systems with deterministic dynamics and random initial conditions. An application to the classical laminar-turbulent transition problem will be presented.    Abstract: Cheng Tai - We present a novel approach to the video super-resolution(SR) problem based on adaptive wavelet frames and elasticity theory. By considering the elastic deformations and the blurring effects together, the proposed is able to model much more realistic object motions in the scene. Adaptive wavelet frame is introduced as a novel regularization in SR problem. It is multi-scale and is adapted to data. Hence it is more flexible than pre-defined sparse regularizations. Both novelties contribute to the improved quality of SR construction results.